# QwtSplinePolynomial - Man Page

A cubic polynomial without constant term.

## Synopsis

`#include <qwt_spline_polynomial.h>`

### Public Member Functions

QwtSplinePolynomial (double c3=0.0, double c2=0.0, double c1=0.0)
Constructor.
bool operator== (const QwtSplinePolynomial &) const
bool operator!= (const QwtSplinePolynomial &) const
double valueAt (double x) const
double slopeAt (double x) const
double curvatureAt (double x) const

### Static Public Member Functions

static QwtSplinePolynomial fromSlopes (const QPointF &p1, double m1, const QPointF &p2, double m2)
static QwtSplinePolynomial fromSlopes (double x, double y, double m1, double m2)
static QwtSplinePolynomial fromCurvatures (const QPointF &p1, double cv1, const QPointF &p2, double cv2)
static QwtSplinePolynomial fromCurvatures (double dx, double dy, double cv1, double cv2)

### Public Attributes

double c3
coefficient of the cubic summand
double c2
double c1
coefficient of the linear summand

## Detailed Description

A cubic polynomial without constant term.

QwtSplinePolynomial is a 3rd degree polynomial of the form: y = c3 * x³ + c2 * x² + c1 * x;

QwtSplinePolynomial is usually used in combination with polygon interpolation, where it is not necessary to store a constant term ( c0 ), as the translation is known from the corresponding polygon points.

QwtSplineC1

Definition at line 30 of file qwt_spline_polynomial.h.

## Constructor & Destructor Documentation

### QwtSplinePolynomial::QwtSplinePolynomial (double a3 = 0.0, double a2 = 0.0, double a1 = 0.0) [inline]

Constructor.

Parameters

a3 Coefficient of the cubic summand
a2 Coefficient of the quadratic summand
a1 Coefficient of the linear summand

Definition at line 77 of file qwt_spline_polynomial.h.

## Member Function Documentation

### double QwtSplinePolynomial::curvatureAt (double x) const [inline]

Calculate the value of the second derivate of a polynomial for a given x

Parameters

x Parameter

Returns

Curvature at x

Definition at line 130 of file qwt_spline_polynomial.h.

### QwtSplinePolynomial QwtSplinePolynomial::fromCurvatures (const QPointF & p1, double cv1, const QPointF & p2, double cv2) [inline], [static]

Find the coefficients for the polynomial including 2 points with specific values for the 2nd derivates at these points.

Parameters

p1 First point
cv1 Value of the second derivate at p1
p2 Second point
cv2 Value of the second derivate at p2

Returns

Coefficients of the polynomials

Note

The missing constant term of the polynomial is p1.y()

Definition at line 185 of file qwt_spline_polynomial.h.

### QwtSplinePolynomial QwtSplinePolynomial::fromCurvatures (double dx, double dy, double cv1, double cv2) [inline], [static]

Find the coefficients for the polynomial from the offset between 2 points and specific values for the 2nd derivates at these points.

Parameters

dx X-offset
dy Y-offset
cv1 Value of the second derivate at p1
cv2 Value of the second derivate at p2

Returns

Coefficients of the polynomials

Definition at line 202 of file qwt_spline_polynomial.h.

### QwtSplinePolynomial QwtSplinePolynomial::fromSlopes (const QPointF & p1, double m1, const QPointF & p2, double m2) [inline], [static]

Find the coefficients for the polynomial including 2 points with specific values for the 1st derivates at these points.

Parameters

p1 First point
m1 Value of the first derivate at p1
p2 Second point
m2 Value of the first derivate at p2

Returns

Coefficients of the polynomials

Note

The missing constant term of the polynomial is p1.y()

Definition at line 147 of file qwt_spline_polynomial.h.

### QwtSplinePolynomial QwtSplinePolynomial::fromSlopes (double dx, double dy, double m1, double m2) [inline], [static]

Find the coefficients for the polynomial from the offset between 2 points and specific values for the 1st derivates at these points.

Parameters

dx X-offset
dy Y-offset
m1 Value of the first derivate at p1
m2 Value of the first derivate at p2

Returns

Coefficients of the polynomials

Definition at line 164 of file qwt_spline_polynomial.h.

### bool QwtSplinePolynomial::operator!= (const QwtSplinePolynomial & other) const [inline]

Parameters

other Other polynomial

Returns

true, when the polynomials have different coefficients

Definition at line 97 of file qwt_spline_polynomial.h.

### bool QwtSplinePolynomial::operator== (const QwtSplinePolynomial & other) const [inline]

Parameters

other Other polynomial

Returns

true, when both polynomials have the same coefficients

Definition at line 88 of file qwt_spline_polynomial.h.

### double QwtSplinePolynomial::slopeAt (double x) const [inline]

Calculate the value of the first derivate of a polynomial for a given x

Parameters

x Parameter

Returns

Slope at x

Definition at line 119 of file qwt_spline_polynomial.h.

### double QwtSplinePolynomial::valueAt (double x) const [inline]

Calculate the value of a polynomial for a given x

Parameters

x Parameter

Returns

Value at x

Definition at line 108 of file qwt_spline_polynomial.h.

## Author

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## Info

Sun Jul 18 2021 Version 6.2.0 Qwt User's Guide